The genome is a unique identifier for human individuals. The genome also contains highly sensitive information, creating a high potential for misuse of genomic data (for example, genetic discrimination). In this paper, I investigated how genomic privacy can be measured in scenarios where an adversary aims to infer a person's genomic markers by constructing probability distributions on the values of genetic variations. I measured the strength of privacy metrics by requiring that metrics are monotonic with increasing adversary strength and uncovered serious problems with several existing metrics currently used to measure genomic privacy. I provide suggestions on metric selection, interpretation, and visualization, and illustrate the work flow using a case study on Alzheimer's disease.